A geometric recipe for twisted superpotentials

We give a pedagogical introduction to spectral networks and abelianization, as well as their relevance to N = 2 supersymmetric field theories in four dimensions. Motivated by a conjecture of Nekrasov-Rosly-Shatashvili, we detail a geometric recipe for computing the effective twisted superpotential for N = 2 field theories of class S as a generating function of the brane of opers, with respect to the spectral coordinates found from abelianization. We present two new examples, the simplest Argyres-Douglas theory and the pure SU(2) gauge theory, while we conjecture the epsilon-expansion of the effective twisted superpotential for the E-6 Minahan-Nemeschansky theory.

Automated summary

In this paper, we provide a pedagogical introduction to spectral networks and abelianization, discussing their relevance to N = 2 supersymmetric field theories in four dimensions. Motivated by a conjecture of Nekrasov-Rosly-Shatashvili, we present a geometric method for computing the effective twisted superpotential for N = 2 field theories of class S. We also introduce two new examples, the simplest Argyres-Douglas theory and the pure SU(2) gauge theory, and propose the epsilon-expansion of the effective twisted superpotential for the E-6 Minahan-Nemeschansky theory.